, Volume 93, Issue 1, pp 35-76

Tannaka-Krein duality for compact matrix pseudogroups. TwistedSU(N) groups

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Summary

The notion of concrete monoidalW *-category is introduced and investigated. A generalization of the Tannaka-Krein duality theorem is proved. It leads to new examples of compact matrix pseudogroups. Among them we have twistedSU(N) groups denoted byS μ U(N). It is shown that the representation theory forS μ U(N) is similar to that ofSU(N): irreducible representations are labeled by Young diagrams and formulae for dimensions and multiplicity are the same as in the classical case.

On leave from Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoza 7400-682, Warsaw, Poland.